Hypothesis Testing of Single Mean and Single Proportion: Additional Information 1.4 2008/06/06 17:37:07 GMT-5 2008/07/18 14:27:20.758 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived α. The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data. If no level of significance is given, we generally can use α=0.05. When you calculate the p-value and draw the picture, the p-value is in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two tailed. The alternate hypothesis, Ha, tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test. Ha never has a symbol that contains an equal sign.The following examples illustrate a left, right, and two-tailed test. H o : μ = 5 H a : μ 5 Test of a single population mean. Ha tells you the test is left-tailed. The picture of the p-value is as follows: H o : p ≤ 0.2 H a : p > 0.2 This is a test of a single population proportion. Ha tells you the test is right-tailed. The picture of the p-value is as follows: H o : μ = 50 H a : μ ≠ 50 This is a test of a single population mean. Ha tells you the test is two-tailed. The picture of the p-value is as follows. Hypothesis Testing Based on sample evidence procedure to determine whether the hypothesis stated is a reasonable statement and cannot be rejected, or is unreasonable and should be rejected. p-value The probability that event will happen purely by chance assuming the null hypothesis is true. The smaller p-value, the stronger the evidence is against the null hypothesis.